Weak hypercharge
The weak hypercharge ( W Engl. Weak, weak) is in particle physics an obtained flavor, that is, a quantum number of elementary particles associated with the weak interaction. With the weak hypercharge can be set to each other in a relationship, the electric charge and the third component of the weak isospin. This is similar to the Gell-Mann - Nishijima relation for the hypercharge of the strong interaction, which is, however, not obtained and the isospin.
Closely related to the weak hypercharge is B -L, the difference of baryon and lepton number.
Definition
It is the generator of the U (1 ) component of the electroweak gauge symmetry group SU (2) × U (1). The associated therewith quantum field B mixes with the W0 component of the electro-weak quantum field W3 and generates the observable gauge bosons Z0 and the photon γ of quantum electrodynamics. The other two components of W3 remain unaffected by the mixing and lead directly to the observable gauge bosons W and W -.
The weak hypercharge is defined by:
After transformation, one obtains for the weak hypercharge:
The weak hypercharge is
- For left-handed leptons, whether loaded or not:
- For left-handed quarks, charged no matter whether positive or negative:
- For right-handed ( charged) leptons:
- For right-handed positively charged quarks:
- For right-handed negatively charged quarks.
(There are no right-handed uncharged leptons, see Goldhaber experiment).
In rare cases, the hypercharge is scaled differently, so then:
B -L
The weak hypercharge is available in the following relationship to B -L, the difference of baryon and lepton number:
Where X is a resulting quantum number of the GUT. Since the weak hypercharge remains well, it means the conservation of baryon number difference - lepton number. This is true for the standard model and most of its extensions.
Neutron decay
Therefore, the neutron decay lepton number L and baryon number B is replaced separately, thus the difference B -L.
Proton decay
The proton decay is a prediction of many GOOD variants.
Therefore, also receives the proton decay B -L, even if neither baryon nor lepton number L B are obtained for itself.
Sources and footnotes
- Particle Physics